Simulated-annealing type Markov chains and their order balance equations

Connors, Daniel P.

doi:10.1109/cdc.1988.194576

Cited by 3 publications

(16 citation statements)

References 6 publications

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“…The timevarying parameter T (t) = 1/β(t) is often referred to as the temperature at time t, and the sequence of T (t) is called cooling schedule. Many proofs of convergence of cooling schedules have already appeared in the literature [4], [10]. We defer discussion of this topic in Section V-B.…”

Section: B Simulated Annealingmentioning

confidence: 99%

“…To verify the optimality of RSA algorithm, we adopt a technical method introduced in [4], in which the optimality of the original simulated annealing algorithm is proven. The authors in [4] have verified the annealing optimal of SA algorithms for a certain class of Markov chains whose transition probabilities can be written as…”

Section: B Optimalitymentioning

confidence: 99%

“…Proof: Our proof for the theorem is based on the technique introduced in [4], in which the annealing optimality of the original SA is proven. We first briefly overview the major steps therein, and apply them to show the optimality of RSA algorithm.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…The authors in [4] consider a class of Markov chains whose transition probabilities can be written as a form of Eq. (3), in which the conventional simulated annealing algorithm can be represented by setting V ij = [f (j) − f (i)] + and ǫ(t) = e −β(t) for achieving minimum f (·).…”

mentioning

confidence: 99%

“…if p = max {c ≥ 0 : ∞ t=1 ǫ(t) c = ∞} Having defined the above terms, we summarize the main results established in [4] as well as in [3], [5], which are valid under the following mild assumptions.…”

mentioning

confidence: 99%

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Simulated Annealing for Optimal Resource Allocation in Wireless Networks with Imperfect Communications

Kwak

Shroff

2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Simulated annealing (SA) method has had significant recent success in designing distributed control algorithms for wireless networks. These SA based techniques formed the basis of new CSMA algorithms and gave rise to the development of numerous variants to achieve the best system performance accommodating different communication technologies and more realistic system conditions. However, these algorithms do not readily extend to networks with noisy environments, as unreliable communication prevents them from gathering the necessary system state information needed to execute the algorithm. In recognition of this challenge, we propose a new SA algorithm that is designed to work more robustly in networks with communications that experience frequent message drops. The main idea of the proposed algorithm is a novel coupling technique that takes into account the external randomness of message passing failure events as a part of probabilistic uncertainty inherent in stochastic acceptance criterion of SA. As a result, the algorithm can be executed even with partial observation of system states, which was not possible under the traditional SA approach. We show that the newly proposed algorithm finds the optimal solution almost surely under the standard annealing framework while offering significant performance benefits in terms of its computational speed in the presence of frequent message drops.The authors are with the Some overheads such as headers and/or guard times may be necessary depending on the types of practical systems, as in [17].

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Section: B Simulated Annealingmentioning

confidence: 99%

Section: B Optimalitymentioning

confidence: 99%

Section: Proof Of Theoremmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Simulated Annealing for Optimal Resource Allocation in Wireless Networks with Imperfect Communications

Kwak

Shroff

2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Quasi-Statically Cooled Markov Chains

Desai

Kumar

1994

Prob. Eng. Inf. Sci.

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We consider time-inhomogeneous Markov chains on a finite state-space, whose transition probabilitiesp,y(/) = Cjjt(t) Vi J are proportional to powers of a vanishing small parameter e(t). We determine the precise relationship between this • chain and the corresponding time-homogeneous chains p,y = c^e 1^, as e ^ 0.Let | vj) be the steady-state distribution of this time-homogeneous chain. We characterize the orders ( JJ,) in v-= Q(e m ). We show that if e(t) \ 0 slowly enough, then the timewise occupation measures /3,-:= sup( 0| SJ1, «(/)* Prob(x(O = /') = +oo J, called the recurrence orders, satisfy ft -fy = ij y -TJ,. Moreover, if S : = [vilvi = min jVj] is the set of ground states of the timehomogeneous chain, thenx(t) -* Q, in an appropriate sense, whenever i/(f) is "cooled" slowly. We also show that there exists a critical p* such that x(t) -> 9 if and only if £,°L, e(t) p * = +oo. We characterize this critical rate as p* = max, e s min,« e S min p = ( , = , 0 , Vv= ,-) maxo s * s/ v-i(K>/ t+1 + Vt k -V,)-Finally, we provide a graph algorithm for determining the orders (%) and (/?,-] and the critical rate p*.

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Tail events of simulated annealing Markov chains

Niemiro

1995

Journal of Applied Probability

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We consider non-homogeneous Markov chains generated by the simulated annealing algorithm. We classify states according to asymptotic properties of trajectories. We identify recurrent and transient states. The set of recurrent states is partitioned into disjoint classes of asymptotically communicating states. These classes correspond to atoms of the tail sigma-field. The results are valid under the weak reversibility assumption of Hajek.

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Simulated-annealing type Markov chains and their order balance equations

Cited by 3 publications

References 6 publications

Simulated Annealing for Optimal Resource Allocation in Wireless Networks with Imperfect Communications

Simulated Annealing for Optimal Resource Allocation in Wireless Networks with Imperfect Communications

Quasi-Statically Cooled Markov Chains

Tail events of simulated annealing Markov chains

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